KVPY SX SB Exam 20141 Question Paper

Question : 20 of 120

Marks: +1, -0

Let X be a set of 5 elements. The number d of ordered pairs (A ,B ) of subsets of X such that

A≠ϕ,B ≠ϕ,A∩B =ϕ

satisfies

Solution:

^5C_2 . 2!+^5C_3(3!/{1!2!}×2!)

+^5C_4[4!/{1!3!}×2!+4!/{2!2!}×2!/2!]

+^5C_5[5!/{1!4!}×2!+5!/{2!3!}×2!]

= 10(2) + 10(6) + 5(8 + 6) + (10 + 20)
= 20 + 60 + 70 + 30 = 180

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